Celery root, also called celeriac, is a very homely bulb with brown, knobbly skin and hard, fibrous white flesh. It tastes like celery with hints of parsley. Despite its ignominious appearance, celery root makes a delicious vegetable gratin, a nice change of pace from potatoes.
Position a rack in the lower third of the oven and preheat to 350 degrees F. Butter an 8x8-inch baking pan and set aside.
Combine the cream, milk, salt, pepper and nutmeg in a medium-size bowl and whisk to blend.
Peel the celery roots and cut in half vertically (lengthwise). Place the flat surface of the root on a cutting board and cut it crosswise into thin slices. Alternately, use a mandoline or food processor to slice the bulbs. Ideally you want the slices to be 1/8-inch thick. Add the slices to the bowl with the cream mixture as you cut them so that they don't discolor.
Neatly arrange the celery root slices in the prepared pan, overlapping them by about one-third. Use all the slices, creating several layers. Pour any remaining cream into the pan. Sprinkle the top of the gratin with the Parmigiano.
Cover the pan tightly with aluminum foil and place the dish on a rimmed baking sheet (to protect your oven from boil-overs). Transfer to the oven and bake for 35 minutes. Remove the foil and continue baking until the celery root is tender when pierced with the tip of a knife, the liquid has been absorbed, and the gratin is golden brown, 15 to 25 minutes longer. If the top browns too quickly, cover it loosely with foil.